The simulation results are depicted on Figure REF 
where we show performance loss, on the Gaussian channel, due to non-VR parts of \(\mathcal {P}(\mathcal {B})\)  for \(LLL\) -reduced random MIMO lattices.
For each point, we average the performance over 1000 random generator matrices \(G\) .
Up to dimension \(n=12\) , considering only the corners of \(\mathcal {P}(\mathcal {B})\)  yields no significant loss in performance.
We can conclude that, on average for the considered model, a \(LLL\) -reduced basis for \(n \le 12\)  is quasi-VR.
However, for larger dimensions, the loss increases and becomes significant.
On the figure, we also added the performance of the dense lattice \(\Lambda _{16}\)  (also called Barnes-Wall lattice in dimension 16 [1]}) for comparison. Obviously, the basis considered in not VR.
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